Manuscript II-B@1 · II-B-v1.tex · section · bfd2eb3c

The clock instrument

Finite names and the destructive clock › The clock instrument · lines 1284–1306

Let

H_{C} = (C^{2})^{\otimes 2}, H_{X} = (C^{2})^{\otimes p_{X}} .

Choose an orthonormal clock basis ${∣ τ_{k} ⟩ : k = 0, 1, 2, 3}$ and put $P_{k} = ∣ τ_{k} ⟩ ⟨ τ_{k} ∣$ . Apply the unitary $B_{C} ∣ τ_{k} ⟩ = ∣ k ⟩$ , followed by computational-basis Enter on both clock names.

Let $R$ be a classical register, with observable algebra

A_{R} = {k = 0 \sum^{3} a_{k} ∣ k ⟩ ⟨ k ∣_{R} : a_{k} \in C} .

Define

D_{k} = ⟨ τ_{k} ∣_{C} \otimes I_{X} .

Displayed formulas in this passage

unlabeled · line 1287
$H_{C} = (C^{2})^{\otimes 2}, H_{X} = (C^{2})^{\otimes p_{X}} .$
unlabeled · line 1298
$A_{R} = {k = 0 \sum^{3} a_{k} ∣ k ⟩ ⟨ k ∣_{R} : a_{k} \in C} .$
unlabeled · line 1303
$D_{k} = ⟨ τ_{k} ∣_{C} \otimes I_{X} .$

Nearby in this section

theorem: Theorem: Complete destructive clock instrument
section: The clock instrument
proposition: Proposition: No return, and record is not residual
section: The clock instrument